The life-cycle hypothesis is based on the assumption that people try to smooth their consumption over their expected adult lifetimes. Suppose Tammy expects to live for another T years and expects to work for R years and earn an annual real income of Y dollars per year.
Tammy will then retire for (T - R) years, and she wants to smooth her annual consumption C and also plans to spend her entire lifetime earnings (R x Y) over the remaining T years. This could be expressed as:
C x T = R x Y.
Note that in class I would have expressed this as:
C x NL = WL x YL
Where NL represents the number of years of life remaining, WL the number of years of working life remaining, and YL the annual real income per year over the WL years of work.
a. Suppose Tammy begins working at age 20, intends to retire at age 65, and expects to live until age 80. If Y = $40,000, what is Tammy's annual C? What is her APC? Her APS?
b. Now suppose Tammy begins her adult life with an initial wealth level equal to W. Consequently, the total amount she will now have available to spend during her lifetime will be
(R x Y + W). If Tammy still wishes to smooth her consumption, then:
C x T = (R x Y) + W
Suppose that W = $120,000 and Y = $40,000. What is Tammy's annual C under these assumptions?
c. Assume now that Y rises to $80,000 and W remains equal to $120,000. What is the MPC out of income (Y)? What is the APC out of wealth (APC_{W})?